# Ilya Khayutin, Mathematics

I am a Veblen Research Instructor at Princeton University and the Institute for Advanced Study since 2016. Before that I was a PhD student at the Einstein Institute of Mathematics at the Hebrew University of Jerusalem under the guidance of Prof. Elon Lindenstrauss.

## Research​

I work in number theory and homogeneous dynamics. My research revolves around equidistribution of arithmetic objects. This is a broad subject that requires a synthesis of ideas from different fields.

In a pursuit to understand equidistribution questions I am studying measure rigidity, arithmetic invariant theory, relative trace formulae and their geometric expansion, sieve methods in multiplicative number theory, subconvexity and large deviations estimates.

## Teaching

In Spring 2019 I am organizing one of Princeton’s junior seminar.

## Papers

• Closed Geodesics on Products of Modular Curves, Ilya Khayutin, 2019, In preparation, tentative abstract

• Non-vanishing of Class Group $L$-functions for Number Fields with a Small Regulator, Ilya Khayutin, 2019, Submitted, arxiv

• Equidistribution on Kuga-Sato Varieties of Torsion Points on CM Elliptic Curves, Ilya Khayutin, 2018, Submitted, arxiv

• Joint Equidistribution of CM Points, Ilya Khayutin, 2017, Annals of Math., arxiv
Videos: 15min talk, 1hr talk

• Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits, Ilya Khayutin, 2015, Accepted at Duke Math J., arxiv

• Large Deviations and Effective Equidistribution, Ilya Khayutin, 2015, Int. Math. Res. Not., arxiv

• Communication with Unobservable Constraints, Ilya Khayutin, 2007, Master’s Thesis, Manuscript

## Contact

email: last name@princeton.edu

Fine Hall 509,
Princeton University.